Add Real Numbers

Section 2.2

P. 74 -79

Properties of Addition

• Commutative Property: - the order in which two numbers are added does NOT change the sum. 4 + -8 = -8 + 4

• Associative Property: The way you group three numbers when adding does NOT change the sum.

(-5 + 8) + 9 = -5 + ( 8 + 9 )

Properties of Addition

• Identity Property: The sum of a number and zero is always the number. -9 + 0 = -9 x + 0 = x

• Inverse Property:

The sum of a number and its opposite is 0. a + (- a ) = 0 -4 + 4 = 0

EXAMPLE 1 Add two integers using a number line

Use a number line to find the sum.

a. – 3 + 6

ANSWER

The final position is 3. So, – 3 + 6 = 3.

EXAMPLE 1

b. – 4 + (– 5)

ANSWER

The final position is – 9. So, – 4 + (– 5) = – 9.

Add two integers using a number line

GUIDED PRACTICE for Example 1

Use a number line to find the sum.

1. 7 +(– 2)

ANSWER

The final position is 3. So, 7 +(– 2) = 5.

Move Units to the left.– 2

End at 5 Start at 7

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

GUIDED PRACTICE for Example 1

Use a number line to find the sum.

3. – 8 + (4)

ANSWER

The final position is – 4. So, – 8 +4 = – 4.

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8

Start at - 8 End at - 4

Move Units to the right.4

GUIDED PRACTICE for Example 1

Use a number line to find the sum.

3. –1 + (– 4)

ANSWER

The final position is – 5. So, – 1 + (– 4) = – 5.

– 7 – 6 – 5 – 4 – 3 – 2 – 1 0

Start at – 1End at – 5

Move Units to the left.– 4

EXAMPLE 2 Add real numbers

Find the sum.

Rule of same signs

Take absolute values.= – (5.3 + 4.9)

= – 10.2 Add.

a. – 5.3 + (– 4.9)

Rule of different signs

Take absolute values. = 19.3 – 12.2

= 7.1 Subtract.

b. 19.3 + (–12.2)

EXAMPLE 3

Identify properties of addition

Statement Property illustrated

a. (x + 9) + 2 = x + (9 + 2) Associative property of addition

b. 8.3 + (– 8.3) = 0 Inverse property of addition

c. – y + 0.7 = 0.7 + (– y) Commutative property of addition

3 11 5

4 2

36 12

8

GUIDED PRACTICE for Examples 2, 3 and 4

Find the sum.

Take absolute values.= – 13.1 + 8.7

= – 4.4

7. – 13.1 + 8.7 Rule of different signs

Identify the property being illustrated.8. 7 + (– 7) = 0 Inverse property of addition

9. – 12 + 0 = – 12 Identity property of addition

10. 4 + 8 = 8 + 4 Commutative property of addition

Subtract.

• Assignment: P. 77 (#1-31)

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